Humanitarian workers described desperate scenes unfolding Thursday at the overwhelmed camp at Idomeni, Greece, where a severe lack of shelter was made worse by a month's worth of rain falling the previous day, according to the U.N. refugee agency.
Many at the camp, about 40% of whom are children, are suffering respiratory problems, the agency added.
Greek officials, who want to clear the camp due to the unsafe conditions, now face the challenge of trying to move thousands of desperate migrants.
"They are living in mud," said George Kiritsis, spokesman for the Greek government's refugee crisis response team.
"It's hard to feed and hard to support people medically."
The crowds were left stranded by Macedonia's decision to close its border to migrants Wednesday.
The closure followed similar moves by other countries along the so-called western Balkan route, the overland path taken by hundreds of thousands of migrants who have entered Europe from Turkey through Greece, on their trek to desirable northern European "destination countries" such as Germany and Sweden.
German Chancellor Angela Merkel criticized the move in an interview with a German public radio station Thursday, describing it as a unilateral action that put undue pressure on Greece, where as many as 42,000 migrants are now stuck without an onward route through Europe.
In what officials said was a collective decision, Slovenia, Croatia and Serbia all closed their borders from midnight Tuesday to migrants without visas or proper authorization to continue along the route.
"Serbia cannot afford to become a collection center for refugees," Serbia's Ministry of Internal Affairs told CNN in an email.
The move brings about an end to the "wave-through" approach which had arisen since the start of Europe's migrant crisis, and a return to regular border controls, officials said.
Merkel told German radio station MDR that closing the route did not solve the problem, and would only put Athens "in a very difficult situation."
She reiterated her calls for a unified European response to the crisis.
Increasing numbers stranded in Greece
The closures had been signaled at the end of an emergency summit between EU heads of government and Turkey
on Monday, when leaders declared that the western Balkans route would be sealed to migrants, bringing an end to irregular migration into Europe.
Governments had been tightening border restrictions along the route for weeks prior to the move, with Macedonia refusing entry to all but Syrians and Iraqis, and allowing only a few hundred or so through a day.
But on the other side of the Greek-Macedonia border, migrants have continued to flood in from Turkey, at an average rate of 1,800 people each day last month.
More than 3,300 arrived in Greece by sea on Wednesday alone, the U.N. refugee agency said.
With migrants refused onward travel through Europe, observers have warned that Greece risks becoming a huge refugee camp
'Soft approach' to clearing overwhelmed camp
They fear scenes such as the ones unfolding at Idomeni, where as many as 14,000 migrants are stranded at a camp only equipped to house 2,400, the U.N. refugee agency said.
The camp has insufficient accommodation, hygiene and lighting, and women and girls there are particularly vulnerable to abuse when the sun sets, said the International Rescue Committee.
Kiritsis, the spokesman for the Greek government's Coordinating Body for Refugee Crisis Management, said officials were taking a "soft approach" in encouraging migrants to voluntarily shift to the south of the country where there were better facilities.
That tactic was better than attempting to forcibly remove them, he said.
"Half are women and children. We won't do that," he said. "We try with flyers and translators. We understand that it will take some time to sink in that they are not moving."
Several buses left Idomeni transporting migrants back to Athens Wednesday, workers at the camp said, but most remained, uncertain of what their options were now.
'Bold' EU-Turkey plan to tackle crisis
At the conclusion of Monday's emergency EU-Turkey summit, leaders announced a bold new proposal to tackle the crisis
Under the suggested "one-for-one" deal, Ankara would take back all migrants who leave Turkey's shores for Europe in the future, on the condition that one Syrian refugee is resettled in Europe for every Syrian returned to Turkey.
The plan would also see the EU provide Turkey with billions in additional funding for refugees, speed up talks on Turkey joining the EU and accelerate the lifting of visa requirements for Turkish citizens in Europe.
Officials still need to hammer out the details of the proposal, elements of which were harshly criticized by international humanitarian groups, before it is sent for approval by EU leaders next week.
European leaders also pledged to provide "massive humanitarian assistance" to Greece -- which is already struggling with a debt crisis -- to help it respond to the unfolding humanitarian crisis within its borders. NATO ships have also been deployed in an effort to smash smuggling networks operating in the Aegean Sea.
Kiritsis said Athens was holding off finalizing its strategy to respond to the crisis until the EU-Turkey plan was confirmed.
Greek officials feared that human traffickers could step up their activities before the EU-Turkey plan was implemented, he said.
More than 1 million arrivals
European leaders are grappling with the biggest refugee crisis since World War II, with more than 1 million people having entered EU territory since the start of 2015.
The majority have come by using trafficking networks to cross the Aegean Sea, which separates Turkey and Greece, with more than 400 migrants dying in that crossing so far this year.
Most of the migrants are from Syria, where the civil war has created more than 4 million refugees.